
Abstract Algebra Abstract Algebra Math Forum 
 LinkBack  Thread Tools  Display Modes 
April 12th, 2014, 12:27 AM  #1 
Member Joined: Sep 2013 Posts: 91 Thanks: 2  Multiplicative inverse in factor ring?
Hello, can someone tell me how to find the multiplicative inverse of an element in a factor ring? Let the element be f and the factor ring T[x]/(m). The basic idea is to solve a diophantine equation like f*um*v=1,right?and we need to find u 
April 12th, 2014, 04:03 AM  #2 
Senior Member Joined: Apr 2014 From: Greater London, England, UK Posts: 320 Thanks: 156 Math Focus: Abstract algebra 
You have the right idea â€“ except that an element of $T[x]/(m)$ is of the form $f+(m)$ where $f$ is a polynomial of degree at most $\deg(m)1$. When you have found a polynomial $u$ such that $fu=1+mv$ for some polynomial $v$, the multiplicative inverse of $f+(m)$ will be $u+(m)$.

April 12th, 2014, 04:05 AM  #3 
Member Joined: Sep 2013 Posts: 91 Thanks: 2 
i see,thanks


Tags 
factor, inverse, multiplicative, ring 
Search tags for this page 
inverses in a quotient ring,quotient ring inverse of element,finding multiplicative inverses in factor rings,how to find inverse of an element in quotient ring,how to find multiplicative inverse in quotient ring,how to find inverse in ring
Click on a term to search for related topics.

Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
multiplicative inverse in modular arithmetic  amnakhan786  Number Theory  1  November 19th, 2012 03:23 AM 
multiplicative inverse using Euclid’s Algorithm  mathslog  Number Theory  7  May 25th, 2012 04:47 AM 
Every member of a multiplicative group is its own inverse  restin84  Number Theory  0  December 15th, 2011 11:11 AM 
factor ring  tinynerdi  Abstract Algebra  3  May 21st, 2010 04:39 AM 
Multiplicative inverse  nightshadengale  Number Theory  2  September 24th, 2007 07:42 PM 